Free Covid tests will be offered to the families of all pupils in England under plans to reopen schools from 8 March.
Rapid test kits will be provided twice a week to pupils and anyone in their household or support bubble regardless of whether they have symptoms.
They will also be available to adults who work with schools, such as bus drivers and after-school club leaders.
Meanwhile, nearly two million people aged 60 to 63 in England are being invited to book their vaccine.
From Monday, people in that age bracket will start receiving letters explaining how to book a jab through the national booking service, NHS England said.
Nearly 20 million people in the UK have now received their first dose, with the government aiming to offer a first dose to all adults by the end of July.
Asked whether vaccine passports or certificates should be used to help open up the economy once this point was reached Chancellor Rishi Sunak told BBC One's Andrew Marr this threw up "complicated, ethical issues".
However, he said the idea could be "relevant" for "reopening parts of our country like mass events" and that a government review was under way.
The chancellor said the rapid progress of the vaccination rollout did not mean coronavirus restrictions could be eased earlier than set out in the prime minister's roadmap and he could not "guarantee" there would be no further lockdowns.
He said he had seen no signs that new variants of the virus were circulating in the country despite cases rising in some parts of England - but stressed it was important people continued following lockdown rules.
Home testing for secondary pupils will be twice weekly, with parents expected to carry out the testing at home after three tests in school. They will be encouraged but not mandatory, with pupils from year one upwards able to take a test, the Department of Health and Social Care said.
Tests will also be available to nursery school staff, the DHSC said.
Public Health England said testing would help "uncover hidden cases" and break chains of transmission and Education Secretary Gavin Williamson said it would "provide yet another layer of reassurance to parents and education staff that schools are as safe as possible".
Tests will be available in-person via workplace testing, at local authority testing sites or through a new ordering service that will allow people to order the kits online to collect.
Anyone who tests positive will need a secondary PCR test to confirm the result of their home test.
Meanwhile, more than three in four people aged between 65 and 70 have now taken up the offer of a vaccine, NHS England said.
Last week, invites began to be sent out to 64-year-olds and those aged 50 to 60 are set to be invited "shortly", the NHS added.
It said the vaccine rollout was gaining "fresh momentum", with medical director Prof Stephen Powis urging anyone who has been invited to take up the offer.
"It doesn't matter when you were invited you can still come forward and protect yourself and others," he said.
The vaccine supplies are expected to increase in March, said Sir Simon Stevens, NHS England chief executive. "We're planning for further acceleration as we head towards Easter."
People can use the national booking service to reserve a slot at NHS vaccination centres or at pharmacies. Those who cannot go online can call 119 free of charge.
NHS teams are also visiting those who cannot travel to a vaccination service.
It comes as leaders from 60 black-majority churches in the UK issued a call to their congregations on Sunday to get the vaccine, urging worshippers to seek out the facts about the vaccine from trusted sources.
Data has suggested people from black and minority ethnic (BAME) backgrounds are being vaccinated at much lower rates than white people.
The Bishop of Dover, the Right Reverend Rose Hudson-Wilkin, who is among the alliance of Christian leaders, said: "Don't let misinformation rob you of your opportunity to protect yourself and others."
The Duke of Cambridge has also urged people to get vaccinated.
According to the government's latest figures, more than 19.6 million people in the UK have now received their first dose - equivalent to more than one in three adults.
The number of people who have had their second jab has risen to 768,810.
Elsewhere, Mr Sunak is preparing to set out details of the Budget on Wednesday as he tries to balance the strains on the public purse caused by the pandemic while supporting those who have been hit the hardest.
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